Theorems · Theorem · order theory
mul_lt_mul_left
∀ {α : Type u_1} [inst : Mul α] [inst_1 : LT α] [i : MulRightStrictMono α] {b c : α}, b < c → ∀ (a : α), b * a < c * a- Cited by
- 17 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulLTMulRightStrictMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulRightStrictMonostatement and proof · cited by 108
- CovariantClass.elimproof · cited by 22
Cited by17
Results whose statement or proof uses this declaration.
- mul_lt_mul_of_lt_of_leproof · cited by 18
- mul_lt_mul_of_lt_of_ltproof · cited by 9
- lt_mul_of_one_lt_left'proof · cited by 3
- Subgroup.exists_isLeast_one_ltproof · cited by 2
- mul_left_strictMonoproof · cited by 1
- StrictMono.mul_const'proof · cited by 1
- mul_lt_of_lt_one_of_leproof · cited by 1
- lt_mul_of_one_lt_of_leproof · cited by 1
- lt_mul_of_one_lt_of_ltproof · cited by 1
- mul_lt_of_lt_one_of_ltproof · cited by 1
- trichotomy_of_mul_eq_mulproof · cited by 0
- cauchy_davenport_mul_of_linearOrder_isCancelMulproof · cited by 0